HIV associated lymphoma continues to complicate the long-term management of HIV/AIDS, and as antiretroviral therapy (ART) has improved, frontline chemotherapy for ARL results in superb outcome. Work from the NIH Clinical Center, for example, has shown that the use of R-EPOCH [etoposide, prednisone, vincristine, cyclophosphamide, and hydroxydaunorubicin used concurrently with rituximab] for ARL, has a complete response rate of 73-91%. The problem of management of HIV infection continues in these patients, suggesting the potential for application of gene transfer in this population. Work from City of Hope has shown in this regard that ARL patients who fail frontline therapy and require myeloablative salvage therapy with autologous peripheral hematopoietic stem and progenitor cell [HSPC] transplantation (HCT) can safely undergo anti-HIV gene therapy with long-term engraftment of gene-marked PBMC. This application will test whether ARL patients receiving the reduced intensity conditioning therapy associated with R-EPOCH can engraft similarly gene-modified autologous HSPC. If so, it is possible that HIV infection itself could select for resistant progeny cells. Thus, the proposed clinical protocol will treat HIV-infected AR patients, following successful completion of R-EPOCH, with autologous HSPC modified with a lentivirus encoding three potent HIV inhibitors with observation during ART interruption (ATI) for effect on HIV infection. The lentivirus vector [called rHIV7-shI-TAR-CCR5RZ ] encodes 3 forms of anti-HIV RNA: RNAi in the form of a short hairpin RNA targeted to an exon in HIV-1 tat/rev (shI), a decoy for the HIV TAT-reactive element (TAR), and a ribozyme that targets the host cell CCR5 chemokine receptor (CCR5RZ). Patients will be enrolled and treated at the NIH Clinical Center and the cell product manufacture and genetic outcome will be performed at City of Hope. Hypotheses: The primary hypothesis is that it is feasible to transplant autologous rHIV7-shI-TAR-CCR5RZ- treated HSPC into patients following treatment with R-EPOCH for ARL and this the procedure is safe. A secondary hypothesis is that the genetically-modified progeny CD4 cells will be protected from HIV and will expand under selective viral pressure during ATI.